Reduction of quasilinear elliptic equations in cylindrical domains with applications

Abstract

Abstract For certain types of semilinear partial differential equations in a cylindrical domain small bounded solutions are known to lie on a so‐called centre manifold of finite dimension. In this paper we prove the result for quasilinear partial differential equations of elliptic and parabolic type. Possible applications include free surface waves and problems in non‐linear elasticity. Here we investigate, pars pro toto, the stationary inviscid potential flow in a channel with a free surface and an obstacle at the bottom.